can i copy game saves from my broken 360 to my computer, than to my new 360 when i get it in

Recentlly my 360 stopped working for me. The 360 will power up with no error lights, but i do not get any video on my tv or any audio. Also none of my wired or wireless controllers or high definition drive will connect. I tried plugging the component cables to a different known working port and still nothing. I bought the protection plan through circuit city and at the moment, i am waiting for them to ship pre paid postage to my house so i can mail my 360 to them. And while talking to their customer service i asked if i could keep my old hard drive so i can keep my saves. but they told me that i have to send in the hard drive as well. so my question is can i somehow save my game saves to my computer that when i get my new 360 can i transfer the saves to it.

Thanks
(p.s. i do not have time to mess with this problem until tomorrow so sorry if it takes me awhile to try any of your guys suggestions)

yeah, open the hard drive casing and take the hard drive out, and connect the sata stuff to your computer and turn your computer on and boot to windows and then you can use xplorer360 and dump an image of the hard drive and then when you get your new hard drive you can copy all the files back and it will work for you, or you can get xsata and do it without having to open the hard drive up